%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC151+1 : TPTP v9.2.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:18:30 PM UTC 2026
% Result : Theorem 0.34s 1.62s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 189)
% Comments :
%------------------------------------------------------------------------------
fof(ax94,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( gt(X1,X2)
=> ~ gt(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax94) ).
fof(ax33,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
=> ~ lt(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax33) ).
fof(ax90,axiom,
! [X1] :
( ssItem(X1)
=> ~ lt(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax90) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ totalorderP(X2)
| totalorderP(X4) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax8,axiom,
! [X1] :
( ssList(X1)
=> ( cyclefreeP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> ~ ( leq(X2,X3)
& leq(X3,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax8) ).
fof(ax10,axiom,
! [X1] :
( ssList(X1)
=> ( strictorderP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> ( lt(X2,X3)
| lt(X3,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax10) ).
fof(ax9,axiom,
! [X1] :
( ssList(X1)
=> ( totalorderP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> ( leq(X2,X3)
| leq(X3,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax9) ).
fof(ax12,axiom,
! [X1] :
( ssList(X1)
=> ( strictorderedP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> lt(X2,X3) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax12) ).
fof(ax11,axiom,
! [X1] :
( ssList(X1)
=> ( totalorderedP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> leq(X2,X3) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax11) ).
fof(ax13,axiom,
! [X1] :
( ssList(X1)
=> ( duplicatefreeP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> X2 != X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax13) ).
fof(ax14,axiom,
! [X1] :
( ssList(X1)
=> ( equalelemsP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(X4,cons(X2,cons(X3,X5))) = X1
=> X2 = X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax14) ).
fof(ax7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(ax44,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( frontsegP(cons(X1,X3),cons(X2,X4))
<=> ( X1 = X2
& frontsegP(X3,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax44) ).
fof(ax56,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( segmentP(X1,X2)
=> segmentP(app(app(X3,X1),X4),X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax56) ).
fof(ax36,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X2,X1)
| memberP(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax36) ).
fof(ax37,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( X1 = X2
| memberP(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(ax82,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax70,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( strictorderedP(cons(X1,X2))
<=> ( nil = X2
| ( nil != X2
& strictorderedP(X2)
& lt(X1,hd(X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax70) ).
fof(ax67,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( totalorderedP(cons(X1,X2))
<=> ( nil = X2
| ( nil != X2
& totalorderedP(X2)
& leq(X1,hd(X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax67) ).
fof(ax50,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( rearsegP(X1,X2)
=> rearsegP(app(X3,X1),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax50) ).
fof(ax43,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(X1,X2)
=> frontsegP(app(X1,X3),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax43) ).
fof(ax95,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( ( gt(X1,X2)
& gt(X2,X3) )
=> gt(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax95) ).
fof(ax88,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( ( geq(X1,X2)
& geq(X2,X3) )
=> geq(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax88) ).
fof(ax34,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( ( lt(X1,X2)
& lt(X2,X3) )
=> lt(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax34) ).
fof(ax91,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( ( leq(X1,X2)
& lt(X2,X3) )
=> lt(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax91) ).
fof(ax30,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( ( leq(X1,X2)
& leq(X2,X3) )
=> leq(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax30) ).
fof(ax53,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X1,X2)
& segmentP(X2,X3) )
=> segmentP(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax53) ).
fof(ax47,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( rearsegP(X1,X2)
& rearsegP(X2,X3) )
=> rearsegP(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax47) ).
fof(ax40,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( frontsegP(X1,X2)
& frontsegP(X2,X3) )
=> frontsegP(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax40) ).
fof(ax6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax6) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax19,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssItem(X4)
=> ( cons(X3,X1) = cons(X4,X2)
=> ( X3 = X4
& X2 = X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax19) ).
fof(ax79,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X2) = app(X1,X2)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax79) ).
fof(ax80,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax80) ).
fof(ax86,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax86) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(ax54,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X1,X2)
& segmentP(X2,X1) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax54) ).
fof(ax48,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( rearsegP(X1,X2)
& rearsegP(X2,X1) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax48) ).
fof(ax41,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( frontsegP(X1,X2)
& frontsegP(X2,X1) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax41) ).
fof(ax87,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( geq(X1,X2)
& geq(X2,X1) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax87) ).
fof(ax29,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( leq(X1,X2)
& leq(X2,X1) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax29) ).
fof(ax93,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
<=> ( X1 != X2
& leq(X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax93) ).
fof(ax92,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( leq(X1,X2)
=> ( X1 = X2
| lt(X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax92) ).
fof(ax35,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( gt(X1,X2)
<=> lt(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax35) ).
fof(ax32,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( geq(X1,X2)
<=> leq(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax32) ).
fof(ax85,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax85) ).
fof(ax77,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( nil != X2
& nil != X1
& hd(X2) = hd(X1)
& tl(X2) = tl(X1) )
=> X2 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax77) ).
fof(ax25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax25) ).
fof(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax1,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax1) ).
fof(ax4,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax73,axiom,
! [X1] :
( ssItem(X1)
=> equalelemsP(cons(X1,nil)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax73) ).
fof(ax71,axiom,
! [X1] :
( ssItem(X1)
=> duplicatefreeP(cons(X1,nil)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax71) ).
fof(ax68,axiom,
! [X1] :
( ssItem(X1)
=> strictorderedP(cons(X1,nil)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax68) ).
fof(ax65,axiom,
! [X1] :
( ssItem(X1)
=> totalorderedP(cons(X1,nil)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax65) ).
fof(ax63,axiom,
! [X1] :
( ssItem(X1)
=> strictorderP(cons(X1,nil)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax63) ).
fof(ax61,axiom,
! [X1] :
( ssItem(X1)
=> totalorderP(cons(X1,nil)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax61) ).
fof(ax59,axiom,
! [X1] :
( ssItem(X1)
=> cyclefreeP(cons(X1,nil)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax59) ).
fof(ax58,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(ax52,axiom,
! [X1] :
( ssList(X1)
=> ( rearsegP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax52) ).
fof(ax46,axiom,
! [X1] :
( ssList(X1)
=> ( frontsegP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax46) ).
fof(ax89,axiom,
! [X1] :
( ssItem(X1)
=> geq(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax89) ).
fof(ax31,axiom,
! [X1] :
( ssItem(X1)
=> leq(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax31) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(ax49,axiom,
! [X1] :
( ssList(X1)
=> rearsegP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax49) ).
fof(ax42,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax42) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(ax51,axiom,
! [X1] :
( ssList(X1)
=> rearsegP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax51) ).
fof(ax45,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax45) ).
fof(ax76,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ? [X2] :
( ssList(X2)
& tl(X1) = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax76) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax75,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ? [X2] :
( ssItem(X2)
& hd(X1) = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax75) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax39) ).
fof(ax2,axiom,
? [X1] :
( ssItem(X1)
& ? [X2] :
( ssItem(X2)
& X1 != X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax2) ).
fof(ax74,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax74) ).
fof(ax72,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax72) ).
fof(ax69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax69) ).
fof(ax66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax66) ).
fof(ax64,axiom,
strictorderP(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax64) ).
fof(ax62,axiom,
totalorderP(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax62) ).
fof(ax60,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax60) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(i_0_96,plain,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( gt(X1,X2)
=> ~ gt(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[ax94]) ).
fof(i_0_97,plain,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
=> ~ lt(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[ax33]) ).
fof(i_0_98,plain,
! [X1] :
( ssItem(X1)
=> ~ lt(X1,X1) ),
inference(fof_simplification,[status(thm)],[ax90]) ).
fof(i_0_99,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
fof(i_0_100,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ totalorderP(X2)
| totalorderP(X4) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(i_0_101,plain,
! [X241,X242,X243,X244,X245,X246] :
( ( ~ cyclefreeP(X241)
| ~ ssItem(X242)
| ~ ssItem(X243)
| ~ ssList(X244)
| ~ ssList(X245)
| ~ ssList(X246)
| app(app(X244,cons(X242,X245)),cons(X243,X246)) != X241
| ~ leq(X242,X243)
| ~ leq(X243,X242)
| ~ ssList(X241) )
& ( ssItem(esk10_1(X241))
| cyclefreeP(X241)
| ~ ssList(X241) )
& ( ssItem(esk11_1(X241))
| cyclefreeP(X241)
| ~ ssList(X241) )
& ( ssList(esk12_1(X241))
| cyclefreeP(X241)
| ~ ssList(X241) )
& ( ssList(esk13_1(X241))
| cyclefreeP(X241)
| ~ ssList(X241) )
& ( ssList(esk14_1(X241))
| cyclefreeP(X241)
| ~ ssList(X241) )
& ( app(app(esk12_1(X241),cons(esk10_1(X241),esk13_1(X241))),cons(esk11_1(X241),esk14_1(X241))) = X241
| cyclefreeP(X241)
| ~ ssList(X241) )
& ( leq(esk10_1(X241),esk11_1(X241))
| cyclefreeP(X241)
| ~ ssList(X241) )
& ( leq(esk11_1(X241),esk10_1(X241))
| cyclefreeP(X241)
| ~ ssList(X241) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax8])])])])]) ).
fof(i_0_102,plain,
! [X263,X264,X265,X266,X267,X268] :
( ( ~ strictorderP(X263)
| ~ ssItem(X264)
| ~ ssItem(X265)
| ~ ssList(X266)
| ~ ssList(X267)
| ~ ssList(X268)
| app(app(X266,cons(X264,X267)),cons(X265,X268)) != X263
| lt(X264,X265)
| lt(X265,X264)
| ~ ssList(X263) )
& ( ssItem(esk20_1(X263))
| strictorderP(X263)
| ~ ssList(X263) )
& ( ssItem(esk21_1(X263))
| strictorderP(X263)
| ~ ssList(X263) )
& ( ssList(esk22_1(X263))
| strictorderP(X263)
| ~ ssList(X263) )
& ( ssList(esk23_1(X263))
| strictorderP(X263)
| ~ ssList(X263) )
& ( ssList(esk24_1(X263))
| strictorderP(X263)
| ~ ssList(X263) )
& ( app(app(esk22_1(X263),cons(esk20_1(X263),esk23_1(X263))),cons(esk21_1(X263),esk24_1(X263))) = X263
| strictorderP(X263)
| ~ ssList(X263) )
& ( ~ lt(esk20_1(X263),esk21_1(X263))
| strictorderP(X263)
| ~ ssList(X263) )
& ( ~ lt(esk21_1(X263),esk20_1(X263))
| strictorderP(X263)
| ~ ssList(X263) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax10])])])])]) ).
fof(i_0_103,plain,
! [X252,X253,X254,X255,X256,X257] :
( ( ~ totalorderP(X252)
| ~ ssItem(X253)
| ~ ssItem(X254)
| ~ ssList(X255)
| ~ ssList(X256)
| ~ ssList(X257)
| app(app(X255,cons(X253,X256)),cons(X254,X257)) != X252
| leq(X253,X254)
| leq(X254,X253)
| ~ ssList(X252) )
& ( ssItem(esk15_1(X252))
| totalorderP(X252)
| ~ ssList(X252) )
& ( ssItem(esk16_1(X252))
| totalorderP(X252)
| ~ ssList(X252) )
& ( ssList(esk17_1(X252))
| totalorderP(X252)
| ~ ssList(X252) )
& ( ssList(esk18_1(X252))
| totalorderP(X252)
| ~ ssList(X252) )
& ( ssList(esk19_1(X252))
| totalorderP(X252)
| ~ ssList(X252) )
& ( app(app(esk17_1(X252),cons(esk15_1(X252),esk18_1(X252))),cons(esk16_1(X252),esk19_1(X252))) = X252
| totalorderP(X252)
| ~ ssList(X252) )
& ( ~ leq(esk15_1(X252),esk16_1(X252))
| totalorderP(X252)
| ~ ssList(X252) )
& ( ~ leq(esk16_1(X252),esk15_1(X252))
| totalorderP(X252)
| ~ ssList(X252) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax9])])])])]) ).
fof(i_0_104,plain,
! [X285,X286,X287,X288,X289,X290] :
( ( ~ strictorderedP(X285)
| ~ ssItem(X286)
| ~ ssItem(X287)
| ~ ssList(X288)
| ~ ssList(X289)
| ~ ssList(X290)
| app(app(X288,cons(X286,X289)),cons(X287,X290)) != X285
| lt(X286,X287)
| ~ ssList(X285) )
& ( ssItem(esk30_1(X285))
| strictorderedP(X285)
| ~ ssList(X285) )
& ( ssItem(esk31_1(X285))
| strictorderedP(X285)
| ~ ssList(X285) )
& ( ssList(esk32_1(X285))
| strictorderedP(X285)
| ~ ssList(X285) )
& ( ssList(esk33_1(X285))
| strictorderedP(X285)
| ~ ssList(X285) )
& ( ssList(esk34_1(X285))
| strictorderedP(X285)
| ~ ssList(X285) )
& ( app(app(esk32_1(X285),cons(esk30_1(X285),esk33_1(X285))),cons(esk31_1(X285),esk34_1(X285))) = X285
| strictorderedP(X285)
| ~ ssList(X285) )
& ( ~ lt(esk30_1(X285),esk31_1(X285))
| strictorderedP(X285)
| ~ ssList(X285) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax12])])])])]) ).
fof(i_0_105,plain,
! [X274,X275,X276,X277,X278,X279] :
( ( ~ totalorderedP(X274)
| ~ ssItem(X275)
| ~ ssItem(X276)
| ~ ssList(X277)
| ~ ssList(X278)
| ~ ssList(X279)
| app(app(X277,cons(X275,X278)),cons(X276,X279)) != X274
| leq(X275,X276)
| ~ ssList(X274) )
& ( ssItem(esk25_1(X274))
| totalorderedP(X274)
| ~ ssList(X274) )
& ( ssItem(esk26_1(X274))
| totalorderedP(X274)
| ~ ssList(X274) )
& ( ssList(esk27_1(X274))
| totalorderedP(X274)
| ~ ssList(X274) )
& ( ssList(esk28_1(X274))
| totalorderedP(X274)
| ~ ssList(X274) )
& ( ssList(esk29_1(X274))
| totalorderedP(X274)
| ~ ssList(X274) )
& ( app(app(esk27_1(X274),cons(esk25_1(X274),esk28_1(X274))),cons(esk26_1(X274),esk29_1(X274))) = X274
| totalorderedP(X274)
| ~ ssList(X274) )
& ( ~ leq(esk25_1(X274),esk26_1(X274))
| totalorderedP(X274)
| ~ ssList(X274) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax11])])])])]) ).
fof(i_0_106,plain,
! [X296,X297,X298,X299,X300,X301] :
( ( ~ duplicatefreeP(X296)
| ~ ssItem(X297)
| ~ ssItem(X298)
| ~ ssList(X299)
| ~ ssList(X300)
| ~ ssList(X301)
| app(app(X299,cons(X297,X300)),cons(X298,X301)) != X296
| X297 != X298
| ~ ssList(X296) )
& ( ssItem(esk35_1(X296))
| duplicatefreeP(X296)
| ~ ssList(X296) )
& ( ssItem(esk36_1(X296))
| duplicatefreeP(X296)
| ~ ssList(X296) )
& ( ssList(esk37_1(X296))
| duplicatefreeP(X296)
| ~ ssList(X296) )
& ( ssList(esk38_1(X296))
| duplicatefreeP(X296)
| ~ ssList(X296) )
& ( ssList(esk39_1(X296))
| duplicatefreeP(X296)
| ~ ssList(X296) )
& ( app(app(esk37_1(X296),cons(esk35_1(X296),esk38_1(X296))),cons(esk36_1(X296),esk39_1(X296))) = X296
| duplicatefreeP(X296)
| ~ ssList(X296) )
& ( esk35_1(X296) = esk36_1(X296)
| duplicatefreeP(X296)
| ~ ssList(X296) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax13])])])])]) ).
fof(i_0_107,plain,
! [X307,X308,X309,X310,X311] :
( ( ~ equalelemsP(X307)
| ~ ssItem(X308)
| ~ ssItem(X309)
| ~ ssList(X310)
| ~ ssList(X311)
| app(X310,cons(X308,cons(X309,X311))) != X307
| X308 = X309
| ~ ssList(X307) )
& ( ssItem(esk40_1(X307))
| equalelemsP(X307)
| ~ ssList(X307) )
& ( ssItem(esk41_1(X307))
| equalelemsP(X307)
| ~ ssList(X307) )
& ( ssList(esk42_1(X307))
| equalelemsP(X307)
| ~ ssList(X307) )
& ( ssList(esk43_1(X307))
| equalelemsP(X307)
| ~ ssList(X307) )
& ( app(esk42_1(X307),cons(esk40_1(X307),cons(esk41_1(X307),esk43_1(X307)))) = X307
| equalelemsP(X307)
| ~ ssList(X307) )
& ( esk40_1(X307) != esk41_1(X307)
| equalelemsP(X307)
| ~ ssList(X307) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax14])])])])]) ).
fof(i_0_108,plain,
! [X235,X236,X239,X240] :
( ( ssList(esk8_2(X235,X236))
| ~ segmentP(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) )
& ( ssList(esk9_2(X235,X236))
| ~ segmentP(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) )
& ( app(app(esk8_2(X235,X236),X236),esk9_2(X235,X236)) = X235
| ~ segmentP(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) )
& ( ~ ssList(X239)
| ~ ssList(X240)
| app(app(X239,X236),X240) != X235
| segmentP(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax7])])])])]) ).
fof(i_0_109,plain,
! [X218,X219,X222,X223] :
( ( ssList(esk3_2(X218,X219))
| ~ memberP(X218,X219)
| ~ ssItem(X219)
| ~ ssList(X218) )
& ( ssList(esk4_2(X218,X219))
| ~ memberP(X218,X219)
| ~ ssItem(X219)
| ~ ssList(X218) )
& ( app(esk3_2(X218,X219),cons(X219,esk4_2(X218,X219))) = X218
| ~ memberP(X218,X219)
| ~ ssItem(X219)
| ~ ssList(X218) )
& ( ~ ssList(X222)
| ~ ssList(X223)
| app(X222,cons(X219,X223)) != X218
| memberP(X218,X219)
| ~ ssItem(X219)
| ~ ssList(X218) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])])]) ).
fof(i_0_110,plain,
! [X374,X375,X376,X377] :
( ( X374 = X375
| ~ frontsegP(cons(X374,X376),cons(X375,X377))
| ~ ssList(X377)
| ~ ssList(X376)
| ~ ssItem(X375)
| ~ ssItem(X374) )
& ( frontsegP(X376,X377)
| ~ frontsegP(cons(X374,X376),cons(X375,X377))
| ~ ssList(X377)
| ~ ssList(X376)
| ~ ssItem(X375)
| ~ ssItem(X374) )
& ( X374 != X375
| ~ frontsegP(X376,X377)
| frontsegP(cons(X374,X376),cons(X375,X377))
| ~ ssList(X377)
| ~ ssList(X376)
| ~ ssItem(X375)
| ~ ssItem(X374) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])])])]) ).
fof(i_0_111,plain,
! [X397,X398,X399,X400] :
( ~ ssList(X397)
| ~ ssList(X398)
| ~ ssList(X399)
| ~ ssList(X400)
| ~ segmentP(X397,X398)
| segmentP(app(app(X399,X397),X400),X398) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])]) ).
fof(i_0_112,plain,
! [X358,X359,X360] :
( ( ~ memberP(app(X359,X360),X358)
| memberP(X359,X358)
| memberP(X360,X358)
| ~ ssList(X360)
| ~ ssList(X359)
| ~ ssItem(X358) )
& ( ~ memberP(X359,X358)
| memberP(app(X359,X360),X358)
| ~ ssList(X360)
| ~ ssList(X359)
| ~ ssItem(X358) )
& ( ~ memberP(X360,X358)
| memberP(app(X359,X360),X358)
| ~ ssList(X360)
| ~ ssList(X359)
| ~ ssItem(X358) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])]) ).
fof(i_0_113,plain,
! [X361,X362,X363] :
( ( ~ memberP(cons(X362,X363),X361)
| X361 = X362
| memberP(X363,X361)
| ~ ssList(X363)
| ~ ssItem(X362)
| ~ ssItem(X361) )
& ( X361 != X362
| memberP(cons(X362,X363),X361)
| ~ ssList(X363)
| ~ ssItem(X362)
| ~ ssItem(X361) )
& ( ~ memberP(X363,X361)
| memberP(cons(X362,X363),X361)
| ~ ssList(X363)
| ~ ssItem(X362)
| ~ ssItem(X361) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])]) ).
fof(i_0_114,plain,
! [X429,X430,X431] :
( ~ ssList(X429)
| ~ ssList(X430)
| ~ ssList(X431)
| app(app(X429,X430),X431) = app(X429,app(X430,X431)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
fof(i_0_115,plain,
! [X339,X340,X341] :
( ~ ssList(X339)
| ~ ssList(X340)
| ~ ssItem(X341)
| cons(X341,app(X340,X339)) = app(cons(X341,X340),X339) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).
fof(i_0_116,plain,
! [X410,X411] :
( ( nil != X411
| nil = X411
| ~ strictorderedP(cons(X410,X411))
| ~ ssList(X411)
| ~ ssItem(X410) )
& ( strictorderedP(X411)
| nil = X411
| ~ strictorderedP(cons(X410,X411))
| ~ ssList(X411)
| ~ ssItem(X410) )
& ( lt(X410,hd(X411))
| nil = X411
| ~ strictorderedP(cons(X410,X411))
| ~ ssList(X411)
| ~ ssItem(X410) )
& ( nil != X411
| strictorderedP(cons(X410,X411))
| ~ ssList(X411)
| ~ ssItem(X410) )
& ( nil = X411
| ~ strictorderedP(X411)
| ~ lt(X410,hd(X411))
| strictorderedP(cons(X410,X411))
| ~ ssList(X411)
| ~ ssItem(X410) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax70])])])]) ).
fof(i_0_117,plain,
! [X407,X408] :
( ( nil != X408
| nil = X408
| ~ totalorderedP(cons(X407,X408))
| ~ ssList(X408)
| ~ ssItem(X407) )
& ( totalorderedP(X408)
| nil = X408
| ~ totalorderedP(cons(X407,X408))
| ~ ssList(X408)
| ~ ssItem(X407) )
& ( leq(X407,hd(X408))
| nil = X408
| ~ totalorderedP(cons(X407,X408))
| ~ ssList(X408)
| ~ ssItem(X407) )
& ( nil != X408
| totalorderedP(cons(X407,X408))
| ~ ssList(X408)
| ~ ssItem(X407) )
& ( nil = X408
| ~ totalorderedP(X408)
| ~ leq(X407,hd(X408))
| totalorderedP(cons(X407,X408))
| ~ ssList(X408)
| ~ ssItem(X407) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax67])])])]) ).
fof(i_0_118,plain,
! [X386,X387,X388] :
( ~ ssList(X386)
| ~ ssList(X387)
| ~ ssList(X388)
| ~ rearsegP(X386,X387)
| rearsegP(app(X388,X386),X387) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax50])])]) ).
fof(i_0_119,plain,
! [X371,X372,X373] :
( ~ ssList(X371)
| ~ ssList(X372)
| ~ ssList(X373)
| ~ frontsegP(X371,X372)
| frontsegP(app(X371,X373),X372) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])]) ).
fof(i_0_120,plain,
! [X455,X456,X457] :
( ~ ssItem(X455)
| ~ ssItem(X456)
| ~ ssItem(X457)
| ~ gt(X455,X456)
| ~ gt(X456,X457)
| gt(X455,X457) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax95])])]) ).
fof(i_0_121,plain,
! [X441,X442,X443] :
( ~ ssItem(X441)
| ~ ssItem(X442)
| ~ ssItem(X443)
| ~ geq(X441,X442)
| ~ geq(X442,X443)
| geq(X441,X443) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax88])])]) ).
fof(i_0_122,plain,
! [X353,X354,X355] :
( ~ ssItem(X353)
| ~ ssItem(X354)
| ~ ssItem(X355)
| ~ lt(X353,X354)
| ~ lt(X354,X355)
| lt(X353,X355) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax34])])]) ).
fof(i_0_123,plain,
! [X446,X447,X448] :
( ~ ssItem(X446)
| ~ ssItem(X447)
| ~ ssItem(X448)
| ~ leq(X446,X447)
| ~ lt(X447,X448)
| lt(X446,X448) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax91])])]) ).
fof(i_0_124,plain,
! [X345,X346,X347] :
( ~ ssItem(X345)
| ~ ssItem(X346)
| ~ ssItem(X347)
| ~ leq(X345,X346)
| ~ leq(X346,X347)
| leq(X345,X347) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax30])])]) ).
fof(i_0_125,plain,
! [X391,X392,X393] :
( ~ ssList(X391)
| ~ ssList(X392)
| ~ ssList(X393)
| ~ segmentP(X391,X392)
| ~ segmentP(X392,X393)
| segmentP(X391,X393) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax53])])]) ).
fof(i_0_126,plain,
! [X380,X381,X382] :
( ~ ssList(X380)
| ~ ssList(X381)
| ~ ssList(X382)
| ~ rearsegP(X380,X381)
| ~ rearsegP(X381,X382)
| rearsegP(X380,X382) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax47])])]) ).
fof(i_0_127,plain,
! [X365,X366,X367] :
( ~ ssList(X365)
| ~ ssList(X366)
| ~ ssList(X367)
| ~ frontsegP(X365,X366)
| ~ frontsegP(X366,X367)
| frontsegP(X365,X367) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax40])])]) ).
fof(i_0_128,plain,
! [X231,X232,X234] :
( ( ssList(esk7_2(X231,X232))
| ~ rearsegP(X231,X232)
| ~ ssList(X232)
| ~ ssList(X231) )
& ( app(esk7_2(X231,X232),X232) = X231
| ~ rearsegP(X231,X232)
| ~ ssList(X232)
| ~ ssList(X231) )
& ( ~ ssList(X234)
| app(X234,X232) != X231
| rearsegP(X231,X232)
| ~ ssList(X232)
| ~ ssList(X231) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])])])]) ).
fof(i_0_129,plain,
! [X227,X228,X230] :
( ( ssList(esk6_2(X227,X228))
| ~ frontsegP(X227,X228)
| ~ ssList(X228)
| ~ ssList(X227) )
& ( app(X228,esk6_2(X227,X228)) = X227
| ~ frontsegP(X227,X228)
| ~ ssList(X228)
| ~ ssList(X227) )
& ( ~ ssList(X230)
| app(X228,X230) != X227
| frontsegP(X227,X228)
| ~ ssList(X228)
| ~ ssList(X227) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])]) ).
fof(i_0_130,plain,
! [X322,X323,X324,X325] :
( ( X324 = X325
| cons(X324,X322) != cons(X325,X323)
| ~ ssItem(X325)
| ~ ssItem(X324)
| ~ ssList(X323)
| ~ ssList(X322) )
& ( X323 = X322
| cons(X324,X322) != cons(X325,X323)
| ~ ssItem(X325)
| ~ ssItem(X324)
| ~ ssList(X323)
| ~ ssList(X322) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax19])])])]) ).
fof(i_0_131,plain,
! [X421,X422,X423] :
( ~ ssList(X421)
| ~ ssList(X422)
| ~ ssList(X423)
| app(X423,X422) != app(X421,X422)
| X423 = X421 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])]) ).
fof(i_0_132,plain,
! [X424,X425,X426] :
( ~ ssList(X424)
| ~ ssList(X425)
| ~ ssList(X426)
| app(X425,X426) != app(X425,X424)
| X426 = X424 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])]) ).
fof(i_0_133,plain,
! [X437,X438] :
( ~ ssList(X437)
| ~ ssList(X438)
| nil = X437
| tl(app(X437,X438)) = app(tl(X437),X438) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).
fof(i_0_134,plain,
! [X427,X428] :
( ~ ssList(X427)
| ~ ssItem(X428)
| cons(X428,X427) = app(cons(X428,nil),X427) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
fof(i_0_135,plain,
! [X394,X395] :
( ~ ssList(X394)
| ~ ssList(X395)
| ~ segmentP(X394,X395)
| ~ segmentP(X395,X394)
| X394 = X395 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax54])])]) ).
fof(i_0_136,plain,
! [X383,X384] :
( ~ ssList(X383)
| ~ ssList(X384)
| ~ rearsegP(X383,X384)
| ~ rearsegP(X384,X383)
| X383 = X384 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax48])])]) ).
fof(i_0_137,plain,
! [X368,X369] :
( ~ ssList(X368)
| ~ ssList(X369)
| ~ frontsegP(X368,X369)
| ~ frontsegP(X369,X368)
| X368 = X369 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax41])])]) ).
fof(i_0_138,plain,
! [X439,X440] :
( ~ ssItem(X439)
| ~ ssItem(X440)
| ~ geq(X439,X440)
| ~ geq(X440,X439)
| X439 = X440 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax87])])]) ).
fof(i_0_139,plain,
! [X343,X344] :
( ~ ssItem(X343)
| ~ ssItem(X344)
| ~ leq(X343,X344)
| ~ leq(X344,X343)
| X343 = X344 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax29])])]) ).
fof(i_0_140,plain,
! [X453,X454] :
( ~ ssItem(X453)
| ~ ssItem(X454)
| ~ gt(X453,X454)
| ~ gt(X454,X453) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_96])])]) ).
fof(i_0_141,plain,
! [X351,X352] :
( ~ ssItem(X351)
| ~ ssItem(X352)
| ~ lt(X351,X352)
| ~ lt(X352,X351) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_97])])]) ).
fof(i_0_142,plain,
! [X451,X452] :
( ( X451 != X452
| ~ lt(X451,X452)
| ~ ssItem(X452)
| ~ ssItem(X451) )
& ( leq(X451,X452)
| ~ lt(X451,X452)
| ~ ssItem(X452)
| ~ ssItem(X451) )
& ( X451 = X452
| ~ leq(X451,X452)
| lt(X451,X452)
| ~ ssItem(X452)
| ~ ssItem(X451) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax93])])])]) ).
fof(i_0_143,plain,
! [X449,X450] :
( ~ ssItem(X449)
| ~ ssItem(X450)
| ~ leq(X449,X450)
| X449 = X450
| lt(X449,X450) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax92])])]) ).
fof(i_0_144,plain,
! [X356,X357] :
( ( ~ gt(X356,X357)
| lt(X357,X356)
| ~ ssItem(X357)
| ~ ssItem(X356) )
& ( ~ lt(X357,X356)
| gt(X356,X357)
| ~ ssItem(X357)
| ~ ssItem(X356) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax35])])])]) ).
fof(i_0_145,plain,
! [X349,X350] :
( ( ~ geq(X349,X350)
| leq(X350,X349)
| ~ ssItem(X350)
| ~ ssItem(X349) )
& ( ~ leq(X350,X349)
| geq(X349,X350)
| ~ ssItem(X350)
| ~ ssItem(X349) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax32])])])]) ).
fof(i_0_146,plain,
! [X435,X436] :
( ~ ssList(X435)
| ~ ssList(X436)
| nil = X435
| hd(app(X435,X436)) = hd(X435) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).
fof(i_0_147,plain,
! [X418,X419] :
( ~ ssList(X418)
| ~ ssList(X419)
| nil = X419
| nil = X418
| hd(X419) != hd(X418)
| tl(X419) != tl(X418)
| X419 = X418 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax77])])]) ).
fof(i_0_148,plain,
! [X335,X336] :
( ~ ssList(X335)
| ~ ssItem(X336)
| tl(cons(X336,X335)) = X335 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])]) ).
fof(i_0_149,plain,
! [X332,X333] :
( ~ ssList(X332)
| ~ ssItem(X333)
| hd(cons(X333,X332)) = X333 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).
fof(i_0_150,plain,
! [X337,X338] :
( ~ ssList(X337)
| ~ ssList(X338)
| ssList(app(X337,X338)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
fof(i_0_151,plain,
! [X318,X319] :
( ~ ssList(X318)
| ~ ssItem(X319)
| ssList(cons(X319,X318)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
fof(i_0_152,plain,
! [X316,X317] :
( ( ~ neq(X316,X317)
| X316 != X317
| ~ ssList(X317)
| ~ ssList(X316) )
& ( X316 = X317
| neq(X316,X317)
| ~ ssList(X317)
| ~ ssList(X316) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
fof(i_0_153,plain,
! [X214,X215] :
( ( ~ neq(X214,X215)
| X214 != X215
| ~ ssItem(X215)
| ~ ssItem(X214) )
& ( X214 = X215
| neq(X214,X215)
| ~ ssItem(X215)
| ~ ssItem(X214) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax1])])])]) ).
fof(i_0_154,plain,
! [X224,X226] :
( ( ssItem(esk5_1(X224))
| ~ singletonP(X224)
| ~ ssList(X224) )
& ( cons(esk5_1(X224),nil) = X224
| ~ singletonP(X224)
| ~ ssList(X224) )
& ( ~ ssItem(X226)
| cons(X226,nil) != X224
| singletonP(X224)
| ~ ssList(X224) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])])]) ).
fof(i_0_155,plain,
! [X432,X433] :
( ( nil = X433
| nil != app(X432,X433)
| ~ ssList(X433)
| ~ ssList(X432) )
& ( nil = X432
| nil != app(X432,X433)
| ~ ssList(X433)
| ~ ssList(X432) )
& ( nil != X433
| nil != X432
| nil = app(X432,X433)
| ~ ssList(X433)
| ~ ssList(X432) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
fof(i_0_156,plain,
! [X320,X321] :
( ~ ssList(X320)
| ~ ssItem(X321)
| cons(X321,X320) != X320 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).
fof(i_0_157,plain,
! [X329,X330] :
( ~ ssList(X329)
| ~ ssItem(X330)
| nil != cons(X330,X329) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).
fof(i_0_158,plain,
! [X326] :
( ( ssList(esk44_1(X326))
| nil = X326
| ~ ssList(X326) )
& ( ssItem(esk45_1(X326))
| nil = X326
| ~ ssList(X326) )
& ( cons(esk45_1(X326),esk44_1(X326)) = X326
| nil = X326
| ~ ssList(X326) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])]) ).
fof(i_0_159,plain,
! [X420] :
( ~ ssList(X420)
| nil = X420
| cons(hd(X420),tl(X420)) = X420 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
fof(i_0_160,plain,
! [X413] :
( ~ ssItem(X413)
| equalelemsP(cons(X413,nil)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax73])]) ).
fof(i_0_161,plain,
! [X412] :
( ~ ssItem(X412)
| duplicatefreeP(cons(X412,nil)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax71])]) ).
fof(i_0_162,plain,
! [X409] :
( ~ ssItem(X409)
| strictorderedP(cons(X409,nil)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax68])]) ).
fof(i_0_163,plain,
! [X406] :
( ~ ssItem(X406)
| totalorderedP(cons(X406,nil)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax65])]) ).
fof(i_0_164,plain,
! [X405] :
( ~ ssItem(X405)
| strictorderP(cons(X405,nil)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax63])]) ).
fof(i_0_165,plain,
! [X404] :
( ~ ssItem(X404)
| totalorderP(cons(X404,nil)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax61])]) ).
fof(i_0_166,plain,
! [X403] :
( ~ ssItem(X403)
| cyclefreeP(cons(X403,nil)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax59])]) ).
fof(i_0_167,plain,
! [X445] :
( ~ ssItem(X445)
| ~ lt(X445,X445) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_98])]) ).
fof(i_0_168,plain,
! [X402] :
( ( ~ segmentP(nil,X402)
| nil = X402
| ~ ssList(X402) )
& ( nil != X402
| segmentP(nil,X402)
| ~ ssList(X402) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax58])])]) ).
fof(i_0_169,plain,
! [X390] :
( ( ~ rearsegP(nil,X390)
| nil = X390
| ~ ssList(X390) )
& ( nil != X390
| rearsegP(nil,X390)
| ~ ssList(X390) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax52])])]) ).
fof(i_0_170,plain,
! [X379] :
( ( ~ frontsegP(nil,X379)
| nil = X379
| ~ ssList(X379) )
& ( nil != X379
| frontsegP(nil,X379)
| ~ ssList(X379) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax46])])]) ).
fof(i_0_171,plain,
! [X364] :
( ~ ssItem(X364)
| ~ memberP(nil,X364) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_99])]) ).
fof(i_0_172,plain,
! [X444] :
( ~ ssItem(X444)
| geq(X444,X444) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax89])]) ).
fof(i_0_173,plain,
! [X348] :
( ~ ssItem(X348)
| leq(X348,X348) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax31])]) ).
fof(i_0_174,plain,
! [X396] :
( ~ ssList(X396)
| segmentP(X396,X396) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])]) ).
fof(i_0_175,plain,
! [X385] :
( ~ ssList(X385)
| rearsegP(X385,X385) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax49])]) ).
fof(i_0_176,plain,
! [X370] :
( ~ ssList(X370)
| frontsegP(X370,X370) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax42])]) ).
fof(i_0_177,plain,
! [X342] :
( ~ ssList(X342)
| app(nil,X342) = X342 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
fof(i_0_178,plain,
! [X434] :
( ~ ssList(X434)
| app(X434,nil) = X434 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
fof(i_0_179,plain,
! [X401] :
( ~ ssList(X401)
| segmentP(X401,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])]) ).
fof(i_0_180,plain,
! [X389] :
( ~ ssList(X389)
| rearsegP(X389,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax51])]) ).
fof(i_0_181,plain,
! [X378] :
( ~ ssList(X378)
| frontsegP(X378,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).
fof(i_0_182,plain,
! [X416] :
( ( ssList(esk47_1(X416))
| nil = X416
| ~ ssList(X416) )
& ( tl(X416) = esk47_1(X416)
| nil = X416
| ~ ssList(X416) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax76])])])]) ).
fof(i_0_183,plain,
! [X334] :
( ~ ssList(X334)
| nil = X334
| ssList(tl(X334)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
fof(i_0_184,plain,
! [X414] :
( ( ssItem(esk46_1(X414))
| nil = X414
| ~ ssList(X414) )
& ( hd(X414) = esk46_1(X414)
| nil = X414
| ~ ssList(X414) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax75])])])]) ).
fof(i_0_185,plain,
! [X331] :
( ~ ssList(X331)
| nil = X331
| ssItem(hd(X331)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
fof(i_0_186,negated_conjecture,
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& totalorderP(esk49_0)
& ~ totalorderP(esk51_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_100])])]) ).
fof(i_0_187,plain,
~ singletonP(nil),
inference(fof_simplification,[status(thm)],[ax39]) ).
fof(i_0_188,plain,
( ssItem(esk1_0)
& ssItem(esk2_0)
& esk1_0 != esk2_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[ax2])]) ).
cnf(i_0_189,plain,
( ~ cyclefreeP(X1)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ leq(X2,X3)
| ~ leq(X3,X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_101]),
[final] ).
cnf(i_0_190,plain,
( lt(X2,X3)
| lt(X3,X2)
| ~ strictorderP(X1)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_191,plain,
( leq(X2,X3)
| leq(X3,X2)
| ~ totalorderP(X1)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_192,plain,
( lt(X2,X3)
| ~ strictorderedP(X1)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_193,plain,
( leq(X2,X3)
| ~ totalorderedP(X1)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_105]),
[final] ).
cnf(i_0_194,plain,
( ~ duplicatefreeP(X1)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| X2 != X3
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_106]),
[final] ).
cnf(i_0_195,plain,
( app(app(esk37_1(X1),cons(esk35_1(X1),esk38_1(X1))),cons(esk36_1(X1),esk39_1(X1))) = X1
| duplicatefreeP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_106]),
[final] ).
cnf(i_0_196,plain,
( app(app(esk32_1(X1),cons(esk30_1(X1),esk33_1(X1))),cons(esk31_1(X1),esk34_1(X1))) = X1
| strictorderedP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_197,plain,
( app(app(esk27_1(X1),cons(esk25_1(X1),esk28_1(X1))),cons(esk26_1(X1),esk29_1(X1))) = X1
| totalorderedP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_105]),
[final] ).
cnf(i_0_198,plain,
( app(app(esk22_1(X1),cons(esk20_1(X1),esk23_1(X1))),cons(esk21_1(X1),esk24_1(X1))) = X1
| strictorderP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_199,plain,
( app(app(esk17_1(X1),cons(esk15_1(X1),esk18_1(X1))),cons(esk16_1(X1),esk19_1(X1))) = X1
| totalorderP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_200,plain,
( app(app(esk12_1(X1),cons(esk10_1(X1),esk13_1(X1))),cons(esk11_1(X1),esk14_1(X1))) = X1
| cyclefreeP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_101]),
[final] ).
cnf(i_0_201,plain,
( X2 = X3
| ~ equalelemsP(X1)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X4)
| ~ ssList(X5)
| app(X4,cons(X2,cons(X3,X5))) != X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_202,plain,
( app(esk42_1(X1),cons(esk40_1(X1),cons(esk41_1(X1),esk43_1(X1)))) = X1
| equalelemsP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_203,plain,
( app(app(esk8_2(X1,X2),X2),esk9_2(X1,X2)) = X1
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_108]),
[final] ).
cnf(i_0_204,plain,
( app(esk3_2(X1,X2),cons(X2,esk4_2(X1,X2))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_109]),
[final] ).
cnf(i_0_205,plain,
( frontsegP(X1,X2)
| ~ frontsegP(cons(X3,X1),cons(X4,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X4)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[i_0_110]),
[final] ).
cnf(i_0_206,plain,
( segmentP(app(app(X3,X1),X4),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ segmentP(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_111]),
[final] ).
cnf(i_0_207,plain,
( X1 = X2
| ~ frontsegP(cons(X1,X3),cons(X2,X4))
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[i_0_110]),
[final] ).
cnf(i_0_208,plain,
( frontsegP(cons(X1,X3),cons(X2,X4))
| X1 != X2
| ~ frontsegP(X3,X4)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[i_0_110]),
[final] ).
cnf(i_0_209,plain,
( memberP(X1,X3)
| memberP(X2,X3)
| ~ memberP(app(X1,X2),X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[i_0_112]),
[final] ).
cnf(i_0_210,plain,
( segmentP(X4,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,X3),X2) != X4
| ~ ssList(X3)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[i_0_108]),
[final] ).
cnf(i_0_211,plain,
( memberP(X4,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,cons(X3,X2)) != X4
| ~ ssItem(X3)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[i_0_109]),
[final] ).
cnf(i_0_212,plain,
( X3 = X1
| memberP(X2,X3)
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[i_0_113]),
[final] ).
cnf(i_0_213,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_214,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[i_0_115]),
[final] ).
cnf(i_0_215,plain,
( nil = X1
| strictorderedP(cons(X2,X1))
| ~ strictorderedP(X1)
| ~ lt(X2,hd(X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_216,plain,
( nil = X1
| totalorderedP(cons(X2,X1))
| ~ totalorderedP(X1)
| ~ leq(X2,hd(X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[i_0_117]),
[final] ).
cnf(i_0_217,plain,
( rearsegP(app(X3,X1),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_118]),
[final] ).
cnf(i_0_218,plain,
( frontsegP(app(X1,X3),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_119]),
[final] ).
cnf(i_0_219,plain,
( memberP(app(X1,X3),X2)
| ~ memberP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[i_0_112]),
[final] ).
cnf(i_0_220,plain,
( memberP(app(X3,X1),X2)
| ~ memberP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[i_0_112]),
[final] ).
cnf(i_0_221,plain,
( memberP(cons(X3,X1),X2)
| ~ memberP(X1,X2)
| ~ ssList(X1)
| ~ ssItem(X3)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[i_0_113]),
[final] ).
cnf(i_0_222,plain,
( lt(X1,hd(X2))
| nil = X2
| ~ strictorderedP(cons(X1,X2))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_223,plain,
( leq(X1,hd(X2))
| nil = X2
| ~ totalorderedP(cons(X1,X2))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[i_0_117]),
[final] ).
cnf(i_0_224,plain,
( gt(X1,X3)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ gt(X1,X2)
| ~ gt(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_120]),
[final] ).
cnf(i_0_225,plain,
( geq(X1,X3)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ geq(X1,X2)
| ~ geq(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_121]),
[final] ).
cnf(i_0_226,plain,
( lt(X1,X3)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ lt(X1,X2)
| ~ lt(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_122]),
[final] ).
cnf(i_0_227,plain,
( lt(X1,X3)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ leq(X1,X2)
| ~ lt(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_123]),
[final] ).
cnf(i_0_228,plain,
( leq(X1,X3)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ leq(X1,X2)
| ~ leq(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_124]),
[final] ).
cnf(i_0_229,plain,
( segmentP(X1,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_125]),
[final] ).
cnf(i_0_230,plain,
( rearsegP(X1,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_126]),
[final] ).
cnf(i_0_231,plain,
( frontsegP(X1,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_127]),
[final] ).
cnf(i_0_232,plain,
( app(esk7_2(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_128]),
[final] ).
cnf(i_0_233,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[i_0_129]),
[final] ).
cnf(i_0_234,plain,
( X1 = X2
| cons(X1,X3) != cons(X2,X4)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[i_0_130]),
[final] ).
cnf(i_0_235,plain,
( X1 = X2
| cons(X3,X2) != cons(X4,X1)
| ~ ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[i_0_130]),
[final] ).
cnf(i_0_236,plain,
( strictorderedP(X1)
| nil = X1
| ~ strictorderedP(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_237,plain,
( totalorderedP(X1)
| nil = X1
| ~ totalorderedP(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[i_0_117]),
[final] ).
cnf(i_0_238,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X3,X2) != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_131]),
[final] ).
cnf(i_0_239,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,X3) != app(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_132]),
[final] ).
cnf(i_0_240,plain,
( ssList(esk9_2(X1,X2))
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_108]),
[final] ).
cnf(i_0_241,plain,
( ssList(esk8_2(X1,X2))
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_108]),
[final] ).
cnf(i_0_242,plain,
( ssList(esk7_2(X1,X2))
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_128]),
[final] ).
cnf(i_0_243,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_129]),
[final] ).
cnf(i_0_244,plain,
( ssList(esk4_2(X1,X2))
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_109]),
[final] ).
cnf(i_0_245,plain,
( ssList(esk3_2(X1,X2))
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_109]),
[final] ).
cnf(i_0_246,plain,
( nil = X1
| tl(app(X1,X2)) = app(tl(X1),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[i_0_133]),
[final] ).
cnf(i_0_247,plain,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[i_0_113]),
[final] ).
cnf(i_0_248,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[i_0_134]),
[final] ).
cnf(i_0_249,plain,
( X1 = X2
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_135]),
[final] ).
cnf(i_0_250,plain,
( X1 = X2
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_136]),
[final] ).
cnf(i_0_251,plain,
( X1 = X2
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_137]),
[final] ).
cnf(i_0_252,plain,
( X1 = X2
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ geq(X1,X2)
| ~ geq(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_138]),
[final] ).
cnf(i_0_253,plain,
( X1 = X2
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ leq(X1,X2)
| ~ leq(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_139]),
[final] ).
cnf(i_0_254,plain,
( rearsegP(X3,X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[i_0_128]),
[final] ).
cnf(i_0_255,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[i_0_129]),
[final] ).
cnf(i_0_256,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ gt(X1,X2)
| ~ gt(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_140]),
[final] ).
cnf(i_0_257,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ lt(X1,X2)
| ~ lt(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_141]),
[final] ).
cnf(i_0_258,plain,
( X1 = X2
| lt(X1,X2)
| ~ leq(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[i_0_142]),
[final] ).
cnf(i_0_259,plain,
( X1 = X2
| lt(X1,X2)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_143]),
[final] ).
cnf(i_0_260,plain,
( strictorderedP(X1)
| ~ lt(esk30_1(X1),esk31_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_261,plain,
( totalorderedP(X1)
| ~ leq(esk25_1(X1),esk26_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_105]),
[final] ).
cnf(i_0_262,plain,
( strictorderP(X1)
| ~ lt(esk21_1(X1),esk20_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_263,plain,
( strictorderP(X1)
| ~ lt(esk20_1(X1),esk21_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_264,plain,
( totalorderP(X1)
| ~ leq(esk16_1(X1),esk15_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_265,plain,
( totalorderP(X1)
| ~ leq(esk15_1(X1),esk16_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_266,plain,
( gt(X2,X1)
| ~ lt(X1,X2)
| ~ ssItem(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[i_0_144]),
[final] ).
cnf(i_0_267,plain,
( geq(X2,X1)
| ~ leq(X1,X2)
| ~ ssItem(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[i_0_145]),
[final] ).
cnf(i_0_268,plain,
( lt(X2,X1)
| ~ gt(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[i_0_144]),
[final] ).
cnf(i_0_269,plain,
( leq(X1,X2)
| ~ lt(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[i_0_142]),
[final] ).
cnf(i_0_270,plain,
( leq(X2,X1)
| ~ geq(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[i_0_145]),
[final] ).
cnf(i_0_271,plain,
( nil = X1
| hd(app(X1,X2)) = hd(X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[i_0_146]),
[final] ).
cnf(i_0_272,plain,
( strictorderedP(cons(X2,X1))
| nil != X1
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_273,plain,
( totalorderedP(cons(X2,X1))
| nil != X1
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[i_0_117]),
[final] ).
cnf(i_0_274,plain,
( nil = X2
| nil = X1
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| hd(X2) != hd(X1)
| tl(X2) != tl(X1) ),
inference(split_conjunct,[status(thm)],[i_0_147]),
[final] ).
cnf(i_0_275,plain,
( tl(cons(X2,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[i_0_148]),
[final] ).
cnf(i_0_276,plain,
( hd(cons(X2,X1)) = X2
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[i_0_149]),
[final] ).
cnf(i_0_277,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[i_0_150]),
[final] ).
cnf(i_0_278,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[i_0_151]),
[final] ).
cnf(i_0_279,plain,
( ~ neq(X1,X2)
| X1 != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_152]),
[final] ).
cnf(i_0_280,plain,
( X1 != X2
| ~ lt(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[i_0_142]),
[final] ).
cnf(i_0_281,plain,
( ~ neq(X1,X2)
| X1 != X2
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[i_0_153]),
[final] ).
cnf(i_0_282,plain,
( singletonP(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[i_0_154]),
[final] ).
cnf(i_0_283,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_155]),
[final] ).
cnf(i_0_284,plain,
( nil = X1
| nil != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[i_0_155]),
[final] ).
cnf(i_0_285,plain,
( leq(esk11_1(X1),esk10_1(X1))
| cyclefreeP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_101]),
[final] ).
cnf(i_0_286,plain,
( leq(esk10_1(X1),esk11_1(X1))
| cyclefreeP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_101]),
[final] ).
cnf(i_0_287,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,X1) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_156]),
[final] ).
cnf(i_0_288,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| nil != cons(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_157]),
[final] ).
cnf(i_0_289,plain,
( cons(esk45_1(X1),esk44_1(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_158]),
[final] ).
cnf(i_0_290,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_159]),
[final] ).
cnf(i_0_291,plain,
( equalelemsP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[i_0_160]),
[final] ).
cnf(i_0_292,plain,
( duplicatefreeP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[i_0_161]),
[final] ).
cnf(i_0_293,plain,
( strictorderedP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[i_0_162]),
[final] ).
cnf(i_0_294,plain,
( totalorderedP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[i_0_163]),
[final] ).
cnf(i_0_295,plain,
( strictorderP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[i_0_164]),
[final] ).
cnf(i_0_296,plain,
( totalorderP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[i_0_165]),
[final] ).
cnf(i_0_297,plain,
( cyclefreeP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[i_0_166]),
[final] ).
cnf(i_0_298,plain,
( cons(esk5_1(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_154]),
[final] ).
cnf(i_0_299,plain,
( nil = app(X2,X1)
| nil != X1
| nil != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[i_0_155]),
[final] ).
cnf(i_0_300,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_152]),
[final] ).
cnf(i_0_301,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[i_0_153]),
[final] ).
cnf(i_0_302,plain,
( ~ ssItem(X1)
| ~ lt(X1,X1) ),
inference(split_conjunct,[status(thm)],[i_0_167]),
[final] ).
cnf(i_0_303,plain,
( nil = X1
| ~ segmentP(nil,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_168]),
[final] ).
cnf(i_0_304,plain,
( nil = X1
| ~ rearsegP(nil,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_169]),
[final] ).
cnf(i_0_305,plain,
( nil = X1
| ~ frontsegP(nil,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_170]),
[final] ).
cnf(i_0_306,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[i_0_171]),
[final] ).
cnf(i_0_307,plain,
( ssItem(esk5_1(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_154]),
[final] ).
cnf(i_0_308,plain,
( equalelemsP(X1)
| esk40_1(X1) != esk41_1(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_309,plain,
( segmentP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_168]),
[final] ).
cnf(i_0_310,plain,
( rearsegP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_169]),
[final] ).
cnf(i_0_311,plain,
( frontsegP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_170]),
[final] ).
cnf(i_0_312,plain,
( ssList(esk43_1(X1))
| equalelemsP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_313,plain,
( ssList(esk42_1(X1))
| equalelemsP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_314,plain,
( ssItem(esk41_1(X1))
| equalelemsP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_315,plain,
( ssItem(esk40_1(X1))
| equalelemsP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_316,plain,
( ssList(esk39_1(X1))
| duplicatefreeP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_106]),
[final] ).
cnf(i_0_317,plain,
( ssList(esk38_1(X1))
| duplicatefreeP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_106]),
[final] ).
cnf(i_0_318,plain,
( ssList(esk37_1(X1))
| duplicatefreeP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_106]),
[final] ).
cnf(i_0_319,plain,
( ssItem(esk36_1(X1))
| duplicatefreeP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_106]),
[final] ).
cnf(i_0_320,plain,
( ssItem(esk35_1(X1))
| duplicatefreeP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_106]),
[final] ).
cnf(i_0_321,plain,
( ssList(esk34_1(X1))
| strictorderedP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_322,plain,
( ssList(esk33_1(X1))
| strictorderedP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_323,plain,
( ssList(esk32_1(X1))
| strictorderedP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_324,plain,
( ssItem(esk31_1(X1))
| strictorderedP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_325,plain,
( ssItem(esk30_1(X1))
| strictorderedP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_326,plain,
( ssList(esk29_1(X1))
| totalorderedP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_105]),
[final] ).
cnf(i_0_327,plain,
( ssList(esk28_1(X1))
| totalorderedP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_105]),
[final] ).
cnf(i_0_328,plain,
( ssList(esk27_1(X1))
| totalorderedP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_105]),
[final] ).
cnf(i_0_329,plain,
( ssItem(esk26_1(X1))
| totalorderedP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_105]),
[final] ).
cnf(i_0_330,plain,
( ssItem(esk25_1(X1))
| totalorderedP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_105]),
[final] ).
cnf(i_0_331,plain,
( ssList(esk24_1(X1))
| strictorderP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_332,plain,
( ssList(esk23_1(X1))
| strictorderP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_333,plain,
( ssList(esk22_1(X1))
| strictorderP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_334,plain,
( ssItem(esk21_1(X1))
| strictorderP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_335,plain,
( ssItem(esk20_1(X1))
| strictorderP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_336,plain,
( ssList(esk19_1(X1))
| totalorderP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_337,plain,
( ssList(esk18_1(X1))
| totalorderP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_338,plain,
( ssList(esk17_1(X1))
| totalorderP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_339,plain,
( ssItem(esk16_1(X1))
| totalorderP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_340,plain,
( ssItem(esk15_1(X1))
| totalorderP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_341,plain,
( ssList(esk14_1(X1))
| cyclefreeP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_101]),
[final] ).
cnf(i_0_342,plain,
( ssList(esk13_1(X1))
| cyclefreeP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_101]),
[final] ).
cnf(i_0_343,plain,
( ssList(esk12_1(X1))
| cyclefreeP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_101]),
[final] ).
cnf(i_0_344,plain,
( ssItem(esk11_1(X1))
| cyclefreeP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_101]),
[final] ).
cnf(i_0_345,plain,
( ssItem(esk10_1(X1))
| cyclefreeP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_101]),
[final] ).
cnf(i_0_346,plain,
( geq(X1,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[i_0_172]),
[final] ).
cnf(i_0_347,plain,
( leq(X1,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[i_0_173]),
[final] ).
cnf(i_0_348,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_174]),
[final] ).
cnf(i_0_349,plain,
( rearsegP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_175]),
[final] ).
cnf(i_0_350,plain,
( frontsegP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_176]),
[final] ).
cnf(i_0_351,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_177]),
[final] ).
cnf(i_0_352,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_178]),
[final] ).
cnf(i_0_353,plain,
( esk35_1(X1) = esk36_1(X1)
| duplicatefreeP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_106]),
[final] ).
cnf(i_0_354,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_179]),
[final] ).
cnf(i_0_355,plain,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_180]),
[final] ).
cnf(i_0_356,plain,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_181]),
[final] ).
cnf(i_0_357,plain,
( ssList(esk47_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_182]),
[final] ).
cnf(i_0_358,plain,
( ssList(esk44_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_158]),
[final] ).
cnf(i_0_359,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_183]),
[final] ).
cnf(i_0_360,plain,
( ssItem(esk46_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_184]),
[final] ).
cnf(i_0_361,plain,
( ssItem(esk45_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_158]),
[final] ).
cnf(i_0_362,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_185]),
[final] ).
cnf(i_0_363,plain,
( tl(X1) = esk47_1(X1)
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_182]),
[final] ).
cnf(i_0_364,plain,
( hd(X1) = esk46_1(X1)
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[i_0_184]),
[final] ).
cnf(i_0_365,negated_conjecture,
~ totalorderP(esk51_0),
inference(split_conjunct,[status(thm)],[i_0_186]),
[final] ).
cnf(i_0_366,plain,
~ singletonP(nil),
inference(split_conjunct,[status(thm)],[i_0_187]),
[final] ).
cnf(i_0_367,plain,
equalelemsP(nil),
inference(split_conjunct,[status(thm)],[ax74]),
[final] ).
cnf(i_0_368,plain,
duplicatefreeP(nil),
inference(split_conjunct,[status(thm)],[ax72]),
[final] ).
cnf(i_0_369,plain,
strictorderedP(nil),
inference(split_conjunct,[status(thm)],[ax69]),
[final] ).
cnf(i_0_370,plain,
totalorderedP(nil),
inference(split_conjunct,[status(thm)],[ax66]),
[final] ).
cnf(i_0_371,plain,
strictorderP(nil),
inference(split_conjunct,[status(thm)],[ax64]),
[final] ).
cnf(i_0_372,negated_conjecture,
totalorderP(esk49_0),
inference(split_conjunct,[status(thm)],[i_0_186]),
[final] ).
cnf(i_0_373,plain,
totalorderP(nil),
inference(split_conjunct,[status(thm)],[ax62]),
[final] ).
cnf(i_0_374,plain,
cyclefreeP(nil),
inference(split_conjunct,[status(thm)],[ax60]),
[final] ).
cnf(i_0_375,negated_conjecture,
ssList(esk51_0),
inference(split_conjunct,[status(thm)],[i_0_186]),
[final] ).
cnf(i_0_376,negated_conjecture,
ssList(esk50_0),
inference(split_conjunct,[status(thm)],[i_0_186]),
[final] ).
cnf(i_0_377,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[i_0_186]),
[final] ).
cnf(i_0_378,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[i_0_186]),
[final] ).
cnf(i_0_379,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]),
[final] ).
cnf(i_0_380,plain,
ssItem(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_188]),
[final] ).
cnf(i_0_381,plain,
ssItem(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_188]),
[final] ).
cnf(i_0_382,plain,
esk1_0 != esk2_0,
inference(split_conjunct,[status(thm)],[i_0_188]),
[final] ).
cnf(i_0_383,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[i_0_186]),
[final] ).
cnf(i_0_384,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[i_0_186]),
[final] ).
cnf(i_0_385,axiom,
X1 = X1 ).
cnf(i_0_386,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_387,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_388,axiom,
( X1 != X2
| app(X1,X3) = app(X2,X3) ) ).
cnf(i_0_389,axiom,
( X1 != X2
| app(X3,X1) = app(X3,X2) ) ).
cnf(i_0_390,axiom,
( X1 != X2
| cons(X1,X3) = cons(X2,X3) ) ).
cnf(i_0_391,axiom,
( X1 != X2
| cons(X3,X1) = cons(X3,X2) ) ).
cnf(i_0_392,axiom,
( X1 != X2
| esk40_1(X1) = esk40_1(X2) ) ).
cnf(i_0_393,axiom,
( X1 != X2
| esk41_1(X1) = esk41_1(X2) ) ).
cnf(i_0_394,axiom,
( X1 != X2
| esk35_1(X1) = esk35_1(X2) ) ).
cnf(i_0_395,axiom,
( X1 != X2
| hd(X1) = hd(X2) ) ).
cnf(i_0_396,axiom,
( X1 != X2
| tl(X1) = tl(X2) ) ).
cnf(i_0_397,axiom,
( X1 != X2
| esk47_1(X1) = esk47_1(X2) ) ).
cnf(i_0_398,axiom,
( X1 != X2
| esk46_1(X1) = esk46_1(X2) ) ).
cnf(i_0_399,axiom,
( X1 != X2
| esk36_1(X1) = esk36_1(X2) ) ).
cnf(i_0_400,axiom,
( X1 != X2
| ~ cyclefreeP(X1)
| cyclefreeP(X2) ) ).
cnf(i_0_401,axiom,
( X1 != X2
| ~ duplicatefreeP(X1)
| duplicatefreeP(X2) ) ).
cnf(i_0_402,axiom,
( X1 != X2
| ~ equalelemsP(X1)
| equalelemsP(X2) ) ).
cnf(i_0_403,axiom,
( X1 != X2
| ~ segmentP(X1,X3)
| segmentP(X2,X3) ) ).
cnf(i_0_404,axiom,
( X1 != X2
| ~ segmentP(X3,X1)
| segmentP(X3,X2) ) ).
cnf(i_0_405,axiom,
( X1 != X2
| ~ memberP(X1,X3)
| memberP(X2,X3) ) ).
cnf(i_0_406,axiom,
( X1 != X2
| ~ memberP(X3,X1)
| memberP(X3,X2) ) ).
cnf(i_0_407,axiom,
( X1 != X2
| ~ frontsegP(X1,X3)
| frontsegP(X2,X3) ) ).
cnf(i_0_408,axiom,
( X1 != X2
| ~ frontsegP(X3,X1)
| frontsegP(X3,X2) ) ).
cnf(i_0_409,axiom,
( X1 != X2
| ~ rearsegP(X1,X3)
| rearsegP(X2,X3) ) ).
cnf(i_0_410,axiom,
( X1 != X2
| ~ rearsegP(X3,X1)
| rearsegP(X3,X2) ) ).
cnf(i_0_411,axiom,
( X1 != X2
| ~ gt(X1,X3)
| gt(X2,X3) ) ).
cnf(i_0_412,axiom,
( X1 != X2
| ~ gt(X3,X1)
| gt(X3,X2) ) ).
cnf(i_0_413,axiom,
( X1 != X2
| ~ geq(X1,X3)
| geq(X2,X3) ) ).
cnf(i_0_414,axiom,
( X1 != X2
| ~ geq(X3,X1)
| geq(X3,X2) ) ).
cnf(i_0_415,axiom,
( X1 != X2
| ~ neq(X1,X3)
| neq(X2,X3) ) ).
cnf(i_0_416,axiom,
( X1 != X2
| ~ neq(X3,X1)
| neq(X3,X2) ) ).
cnf(i_0_417,axiom,
( X1 != X2
| ~ singletonP(X1)
| singletonP(X2) ) ).
cnf(i_0_418,axiom,
( X1 != X2
| ~ ssItem(X1)
| ssItem(X2) ) ).
cnf(i_0_419,axiom,
( X1 != X2
| ~ ssList(X1)
| ssList(X2) ) ).
cnf(i_0_420,axiom,
( X1 != X2
| ~ leq(X1,X3)
| leq(X2,X3) ) ).
cnf(i_0_421,axiom,
( X1 != X2
| ~ leq(X3,X1)
| leq(X3,X2) ) ).
cnf(i_0_422,axiom,
( X1 != X2
| ~ lt(X1,X3)
| lt(X2,X3) ) ).
cnf(i_0_423,axiom,
( X1 != X2
| ~ lt(X3,X1)
| lt(X3,X2) ) ).
cnf(i_0_424,axiom,
( X1 != X2
| ~ strictorderP(X1)
| strictorderP(X2) ) ).
cnf(i_0_425,axiom,
( X1 != X2
| ~ totalorderP(X1)
| totalorderP(X2) ) ).
cnf(i_0_426,axiom,
( X1 != X2
| ~ strictorderedP(X1)
| strictorderedP(X2) ) ).
cnf(i_0_427,axiom,
( X1 != X2
| ~ totalorderedP(X1)
| totalorderedP(X2) ) ).
cnf(i_0_385_001,axiom,
X1 = X1 ).
cnf(i_0_386_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_387_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_388_004,axiom,
( X1 != X2
| app(X1,X3) = app(X2,X3) ) ).
cnf(i_0_389_005,axiom,
( X1 != X2
| app(X3,X1) = app(X3,X2) ) ).
cnf(i_0_390_006,axiom,
( X1 != X2
| cons(X1,X3) = cons(X2,X3) ) ).
cnf(i_0_391_007,axiom,
( X1 != X2
| cons(X3,X1) = cons(X3,X2) ) ).
cnf(i_0_392_008,axiom,
( X1 != X2
| esk40_1(X1) = esk40_1(X2) ) ).
cnf(i_0_393_009,axiom,
( X1 != X2
| esk41_1(X1) = esk41_1(X2) ) ).
cnf(i_0_394_010,axiom,
( X1 != X2
| esk35_1(X1) = esk35_1(X2) ) ).
cnf(i_0_395_011,axiom,
( X1 != X2
| hd(X1) = hd(X2) ) ).
cnf(i_0_396_012,axiom,
( X1 != X2
| tl(X1) = tl(X2) ) ).
cnf(i_0_397_013,axiom,
( X1 != X2
| esk47_1(X1) = esk47_1(X2) ) ).
cnf(i_0_398_014,axiom,
( X1 != X2
| esk46_1(X1) = esk46_1(X2) ) ).
cnf(i_0_399_015,axiom,
( X1 != X2
| esk36_1(X1) = esk36_1(X2) ) ).
cnf(i_0_400_016,axiom,
( X1 != X2
| ~ cyclefreeP(X1)
| cyclefreeP(X2) ) ).
cnf(i_0_401_017,axiom,
( X1 != X2
| ~ duplicatefreeP(X1)
| duplicatefreeP(X2) ) ).
cnf(i_0_402_018,axiom,
( X1 != X2
| ~ equalelemsP(X1)
| equalelemsP(X2) ) ).
cnf(i_0_403_019,axiom,
( X1 != X2
| ~ segmentP(X1,X3)
| segmentP(X2,X3) ) ).
cnf(i_0_404_020,axiom,
( X1 != X2
| ~ segmentP(X3,X1)
| segmentP(X3,X2) ) ).
cnf(i_0_405_021,axiom,
( X1 != X2
| ~ memberP(X1,X3)
| memberP(X2,X3) ) ).
cnf(i_0_406_022,axiom,
( X1 != X2
| ~ memberP(X3,X1)
| memberP(X3,X2) ) ).
cnf(i_0_407_023,axiom,
( X1 != X2
| ~ frontsegP(X1,X3)
| frontsegP(X2,X3) ) ).
cnf(i_0_408_024,axiom,
( X1 != X2
| ~ frontsegP(X3,X1)
| frontsegP(X3,X2) ) ).
cnf(i_0_409_025,axiom,
( X1 != X2
| ~ rearsegP(X1,X3)
| rearsegP(X2,X3) ) ).
cnf(i_0_410_026,axiom,
( X1 != X2
| ~ rearsegP(X3,X1)
| rearsegP(X3,X2) ) ).
cnf(i_0_411_027,axiom,
( X1 != X2
| ~ gt(X1,X3)
| gt(X2,X3) ) ).
cnf(i_0_412_028,axiom,
( X1 != X2
| ~ gt(X3,X1)
| gt(X3,X2) ) ).
cnf(i_0_413_029,axiom,
( X1 != X2
| ~ geq(X1,X3)
| geq(X2,X3) ) ).
cnf(i_0_414_030,axiom,
( X1 != X2
| ~ geq(X3,X1)
| geq(X3,X2) ) ).
cnf(i_0_415_031,axiom,
( X1 != X2
| ~ neq(X1,X3)
| neq(X2,X3) ) ).
cnf(i_0_416_032,axiom,
( X1 != X2
| ~ neq(X3,X1)
| neq(X3,X2) ) ).
cnf(i_0_417_033,axiom,
( X1 != X2
| ~ singletonP(X1)
| singletonP(X2) ) ).
cnf(i_0_418_034,axiom,
( X1 != X2
| ~ ssItem(X1)
| ssItem(X2) ) ).
cnf(i_0_419_035,axiom,
( X1 != X2
| ~ ssList(X1)
| ssList(X2) ) ).
cnf(i_0_420_036,axiom,
( X1 != X2
| ~ leq(X1,X3)
| leq(X2,X3) ) ).
cnf(i_0_421_037,axiom,
( X1 != X2
| ~ leq(X3,X1)
| leq(X3,X2) ) ).
cnf(i_0_422_038,axiom,
( X1 != X2
| ~ lt(X1,X3)
| lt(X2,X3) ) ).
cnf(i_0_423_039,axiom,
( X1 != X2
| ~ lt(X3,X1)
| lt(X3,X2) ) ).
cnf(i_0_424_040,axiom,
( X1 != X2
| ~ strictorderP(X1)
| strictorderP(X2) ) ).
cnf(i_0_425_041,axiom,
( X1 != X2
| ~ totalorderP(X1)
| totalorderP(X2) ) ).
cnf(i_0_426_042,axiom,
( X1 != X2
| ~ strictorderedP(X1)
| strictorderedP(X2) ) ).
cnf(i_0_427_043,axiom,
( X1 != X2
| ~ totalorderedP(X1)
| totalorderedP(X2) ) ).
cnf(i_0_428,plain,
( ~ leq(X1,X2)
| ~ leq(X2,X1)
| ~ ssList(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| ~ cyclefreeP(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssList(X5) ),
inference(equality_inference,[],[189]) ).
cnf(i_0_429,plain,
( lt(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(app(app(X3,cons(X2,X4)),cons(X1,X5)))
| lt(X2,X1)
| ~ strictorderP(app(app(X3,cons(X2,X4)),cons(X1,X5)))
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssList(X5) ),
inference(equality_inference,[],[190]) ).
cnf(i_0_430,plain,
( leq(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(app(app(X3,cons(X2,X4)),cons(X1,X5)))
| leq(X2,X1)
| ~ totalorderP(app(app(X3,cons(X2,X4)),cons(X1,X5)))
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssList(X5) ),
inference(equality_inference,[],[191]) ).
cnf(i_0_431,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| lt(X1,X2)
| ~ strictorderedP(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssList(X5) ),
inference(equality_inference,[],[192]) ).
cnf(i_0_432,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| leq(X1,X2)
| ~ totalorderedP(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssList(X5) ),
inference(equality_inference,[],[193]) ).
cnf(i_0_433,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(app(X3,cons(X1,cons(X2,X4))))
| X1 = X2
| ~ equalelemsP(app(X3,cons(X1,cons(X2,X4))))
| ~ ssList(X3)
| ~ ssList(X4) ),
inference(equality_inference,[],[201]) ).
cnf(i_0_434,plain,
( ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X3)
| ~ ssItem(X3)
| frontsegP(cons(X3,X1),cons(X3,X2)) ),
inference(equality_inference,[],[208]) ).
cnf(i_0_435,plain,
( ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3))
| segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(equality_inference,[],[210]) ).
cnf(i_0_436,plain,
( ~ ssItem(X1)
| ~ ssList(app(X2,cons(X1,X3)))
| memberP(app(X2,cons(X1,X3)),X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(equality_inference,[],[211]) ).
cnf(i_0_437,plain,
( ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X2)
| X1 = X1 ),
inference(equality_inference,[],[234]) ).
cnf(i_0_438,plain,
( ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X2)
| X2 = X2 ),
inference(equality_inference,[],[235]) ).
cnf(i_0_439,plain,
( ~ ssList(X1)
| ~ ssList(X1)
| X1 = X1
| ~ ssList(X2) ),
inference(equality_inference,[],[238]) ).
cnf(i_0_440,plain,
( ~ ssList(X1)
| ~ ssList(X1)
| X1 = X1
| ~ ssList(X2) ),
inference(equality_inference,[],[239]) ).
cnf(i_0_441,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssItem(X2)
| memberP(cons(X2,X1),X2) ),
inference(equality_inference,[],[247]) ).
cnf(i_0_442,plain,
( ~ ssList(X1)
| ~ ssList(app(X2,X1))
| rearsegP(app(X2,X1),X1)
| ~ ssList(X2) ),
inference(equality_inference,[],[254]) ).
cnf(i_0_443,plain,
( ~ ssList(X1)
| ~ ssList(app(X1,X2))
| frontsegP(app(X1,X2),X1)
| ~ ssList(X2) ),
inference(equality_inference,[],[255]) ).
cnf(i_0_444,plain,
( ~ ssList(nil)
| ~ ssItem(X1)
| strictorderedP(cons(X1,nil)) ),
inference(equality_inference,[],[272]) ).
cnf(i_0_445,plain,
( ~ ssList(nil)
| ~ ssItem(X1)
| totalorderedP(cons(X1,nil)) ),
inference(equality_inference,[],[273]) ).
cnf(i_0_446,plain,
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(equality_inference,[],[279]) ).
cnf(i_0_447,plain,
( ~ lt(X1,X1)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_inference,[],[280]) ).
cnf(i_0_448,plain,
( ~ ssItem(X1)
| ~ ssItem(X1)
| ~ neq(X1,X1) ),
inference(equality_inference,[],[281]) ).
cnf(i_0_449,plain,
( ~ ssList(cons(X1,nil))
| singletonP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(equality_inference,[],[282]) ).
cnf(i_0_450,plain,
( ~ ssList(nil)
| segmentP(nil,nil) ),
inference(equality_inference,[],[309]) ).
cnf(i_0_451,plain,
( ~ ssList(nil)
| rearsegP(nil,nil) ),
inference(equality_inference,[],[310]) ).
cnf(i_0_452,plain,
( ~ ssList(nil)
| frontsegP(nil,nil) ),
inference(equality_inference,[],[311]) ).
cnf(i_0_453,plain,
geq(esk2_0,esk2_0),
inference(scs_inference,[],[i_0_380,i_0_346]) ).
cnf(i_0_454,plain,
( ~ ssItem(X1)
| geq(X1,X1) ),
inference(rename_variables,[],[i_0_346]) ).
cnf(i_0_455,plain,
leq(esk2_0,esk2_0),
inference(scs_inference,[],[i_0_380,i_0_346,i_0_347]) ).
cnf(i_0_456,plain,
( ~ ssItem(X1)
| leq(X1,X1) ),
inference(rename_variables,[],[i_0_347]) ).
cnf(i_0_457,plain,
segmentP(esk51_0,esk51_0),
inference(scs_inference,[],[i_0_375,i_0_380,i_0_346,i_0_347,i_0_348]) ).
cnf(i_0_458,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(rename_variables,[],[i_0_348]) ).
cnf(i_0_459,plain,
rearsegP(esk51_0,esk51_0),
inference(scs_inference,[],[i_0_375,i_0_380,i_0_346,i_0_347,i_0_348,i_0_349]) ).
cnf(i_0_460,plain,
( ~ ssList(X1)
| rearsegP(X1,X1) ),
inference(rename_variables,[],[i_0_349]) ).
cnf(i_0_461,plain,
frontsegP(esk51_0,esk51_0),
inference(scs_inference,[],[i_0_375,i_0_380,i_0_346,i_0_347,i_0_348,i_0_349,i_0_350]) ).
cnf(i_0_462,plain,
( ~ ssList(X1)
| frontsegP(X1,X1) ),
inference(rename_variables,[],[i_0_350]) ).
cnf(i_0_463,plain,
esk51_0 = esk49_0,
inference(scs_inference,[],[i_0_375,i_0_383,i_0_380,i_0_346,i_0_347,i_0_348,i_0_349,i_0_350,i_0_386]) ).
cnf(i_0_464,plain,
~ neq(esk51_0,esk51_0),
inference(scs_inference,[],[i_0_375,i_0_383,i_0_380,i_0_346,i_0_347,i_0_348,i_0_349,i_0_350,i_0_386,i_0_446]) ).
cnf(i_0_465,plain,
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(rename_variables,[],[i_0_446]) ).
cnf(i_0_466,plain,
$false,
inference(scs_inference,[],[i_0_365,i_0_372,i_0_375,i_0_383,i_0_380,i_0_346,i_0_347,i_0_348,i_0_349,i_0_350,i_0_386,i_0_446,i_0_425]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC151+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n016.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:30:51 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.34/1.62 % Version : CSE_E---1.7
% 0.34/1.62 % Problem : theBenchmark.p
% 0.34/1.62 % SZS status Theorem for theBenchmark.p
% 0.34/1.62 % SZS output start CNFRefutation
% See solution above
% 0.44/1.70 % Total time : 1.271s
%------------------------------------------------------------------------------